One-dimensional lattice dynamics of the diffusion-limited reaction A + A → A + S: Transient behavior

Journal of Statistical Physics

Volumn 99, Issue 5-6, 2000, Pages 1397-1407

  Abad, Enrique ^a   Frisch, Harry L ^b   Nicolis, Gregoire ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

Cellular automata; Differential difference equations; Nonequilibrium reaction diffusion systems

Indexed keywords

EID: 0034195323     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018649108442     Document Type: Article

References (18)

1. D. ben Avraham, M. Burschka, and C. Doering, J. Stat. Phys. 60:695 (1990).
2. E. Abad, G. Nicolis, and P. Grosfils, Nonlinear reactive systems viewed as stochastic dynamical systems, unpublished.
3. V. Privman, Phys. Rev. E 50:50 (1994).
4. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
5. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
6. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
7. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
8. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
9. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
10. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
11. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
12. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
13. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
14. See J. L. Spouge, Phys. Rev. Lett. 60:871 (1988) when initial "concentration" ρ is 1/2; for the case with reverse reaction see J. C. Lin, C. R. Doering, and D. ben-Avraham, Chem. Phys. 146:355 (1990). There exist some exact solutions of the equivalent diffusion-annihilation process A + A → S + S, see, e.g., R. J. Glauber, J. Math. Phys. 4:294 (1963); T. Liggett, Interacting Particle Systems (Springer-Verlag, New York, 1985); S. Redner and K. Kang, Phys. Rev. A 32:435 (1985); A. A. Lushnikov, Phys. Lett. A 120:135 (1987); V. Kuzokov and E. Kotomin, Rep. Prog. 87:1941 (1988); M. Bramson and J. Lebowitz, Phys. Rev. Lett. 61:2397 (1988); D. Balding, P. Clifford, and N. J. B. Green, Phys. Lett. A 126:481 (1988); F. Family and J. G. Amar, J. Stat. Phys. 65:1235 (1991); M. D. Grynberg and Robin B. Stinchcombe, Phys. Rev. Lett. 76:851 (1996) and references therein.
15. J. Crank, The Mathematics of Diffusion, 2nd ed. reprinted (Clarendon, Oxford, 1976).
16. I. M. Ryshik and I. S. Gradstein, Tables of Series, Products and Integrals, 2nd ed. (VEB Deutscher Verlag der Wissenschaften, Berlin, 1963).
17. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. (Clarendon, Oxford, 1959).
18. G. Doetsch, Theorie und Anwendung der Laplace Transformation (Dover Pub., New York, 1943).